Reportedly influenced by material (5)
I believe the answer is:
suede
'material' is the definition.
(I know that suede is a type of material)
'reportedly influenced' is the wordplay.
'reportedly' shows a homophone (sound like).
'influenced' becomes 'swayed' (swaying is a kind of influencing).
'swayed' is a homophone of 'SUEDE'.
'by' is the link.
(Other definitions for suede that I've seen before include "Undressed kidskin" , "Leather with a soft napped surface" , "Leather with velvety nap used in shoes and clothes" , "Brushed leather" , "leather material" .)